Breaking a one-parameter 'poor man's' scaling approach in the Luttinger liquid. (8th August 2018)

• Record Type: Journal Article
• Authors: Afonin, V V; Petrov, V Yu
• Is Part Of: Journal of physics. Volume 30:Number 35(2018)
• Publication Date: 2018-08-08
• Subjects: Luttinger model -- functional bosonization -- 'poor man's' scaling approach; Condensed matter -- Periodicals; Matière condensée -- Périodiques; Vaste stoffen; Vloeistoffen; Natuurkunde; Electronic journals; Computer network resources; 530.4105
• DOI: 10.1088/1361-648X/aad515
• Languages: English
• ISSNs: 0953-8984

Abstract

Abstract: Using a previously derived effective theory we explore the conductance in the Luttinger model with one impurity. A new approach to the renormalization group (RG) analysis of this model is developed. It is based on the original Gell-Mann–Low formulation of RG. We sum up infrared logarithmic contributions to conductance in the leading and a few subsequent approximations. We analyze the validity of the widely used 'poor man's' scaling approach and find that it is applicable only in the leading approximation. Our results for corrections to this approximation are different from results obtained in other papers. This should be expected beforehand, as the Gell-Mann–Low function of the model is not regularization scheme invariant. For this reason the observed quantity (e.g. conductance) can not satisfy the Gell-Mann–Low equation beyond the 'leading-log' approximation as it is supposed in the 'poor man's' approach. We formulate the method to calculate the conductance from the renormalized hamiltonian in post-leading approximations and match our results to the case of weak impurity where the answer is known in any order of electron–electron interaction.